Singularities and qualitative study in LQC

We will perform a detailed analysis of singularities in Einstein Cosmology and in LQC (Loop Quantum Cosmology). We will obtain explicit analytical expressions for the energy density and the Hubble constant for a given set of possible Equations of State. We will also consider the case when the background is driven by a single scalar field, obtaining analytical expressions for the corresponding potential. And, in a given particular case, we will perform a qualitative study of the orbits in the associated phase space of the scalar. eld

Note on the reheating temperature in Starobinsky-type potentials

The relation between the reheating temperature, the number of e-folds and the spectral index is shown for the Starobinsky model and some of its descendants through a very detailed calculation of these three quantities. The conclusion is that for viable temperatures between $1$ MeV and $10^9$ GeV the corresponding values of the spectral index enter perfectly in its $2sigma$ C.L., which shows the viability of this kind of models.Comment: Version accepted for publication in GER

The spectrum of Gravitational Waves, their overproduction in quintessential inflation and its influence in the reheating temperature

One of the most important issues in an inflationary theory as standard or quintessential inflation is the mechanism to reheat the universe after the end of the inflationary period in order to match with the Hot Big Bang universe. In quintessential inflation two mechanisms are frequently used, namely the reheating via gravitational particle production which is, as we will see, very efficient when the phase transition from the end of inflation to a kinetic regime (all the energy of the inflaton field is kinetic) is very abrupt, and the so-called instant preheating which is used for a very smooth phase transition because in that case the gravitational particle production is very inefficient. In the present work, a detailed study of these mechanisms is done, obtaining bounds for the reheating temperature and the range of the parameters involved in each reheating mechanism in order that the Gravitational Waves (GWs) produced at the beginning of kination do not disturb the Big Bang Nucleosynthesis (BBN) success.Comment: 51 pages, 4 figures, 1 table, new material and references added. Version accepted for publication in Univers

Cosmological solutions in spatially curved universes with adiabatic particle production

We perform a qualitative and thermodynamic study of two models when one takes into account adiabatic particle production. In the first one, there is a constant particle production rate, which leads to solutions depicting the current cosmic acceleration but without inflation. The other one has solutions that unify the early and late time acceleration. These solutions converge asymptotically to the thermal equilibrium.Comment: 13 pages, 10 figures. Version accepted for publication in CQ

Reheating via gravitational particle production in simple models of quintessence or Λ\LambdaCDM inflation

We have tested some simple $\Lambda$CDM (the same test is also valid for quintessence) inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck's team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success.Comment: Proceedings of the workshop "Cosmology and the Quantum Vacuum IV" Segovia, Spain. Accepted for publication in the special Issue "Cosmology and the Quantum Vacuum" of Galaxie

Quintessential inflation at low reheating temperatures

We have tested some simple quintessential inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck's team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success. Moreover, for the models coming from supergravity one needs to demand low temperatures in order to avoid problems such as the gravitino overproduction or the gravitational production of moduli fields, which are obtained only when the reheating temperature is due to the production of massless particles with a coupling constant very close to its conformal value.Comment: 21 pages, 10 figures. Version accepted for publication in EPJ

Reheating constraints in quintessential inflation

We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced in cite{hap, hap2}, we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data cite{Ade, Planck, bicep2} is only possible for reheating temperatures that range between $1$ GeV and $10^4$ GeV. On the other hand, when the universe reheats via the production of massless particles, the viability of the model is only possible when those particles are nearly conformally coupled with gravity, leading to a reheating temperature between $1$ MeV and $10^4$ GeV.Comment: Version accepted for publication in PR

The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology

We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.Comment: 39 pages, 19 figures. Version accepted for publication in JCA

Understanding gravitational particle production in quintessential inflation

The diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article we show that, in order that the overproduction of Gravitational Waves (GWs) during this phase transition does not disturb the Big Bang Nucleosynthesis (BBN) success, the decay has to be produced after the end of the kination regime, obtaining a maximum reheating temperature in the TeV regime.Comment: 18 pages, 5 figures. Version accepted for publication in JCA